@zx81 it probably is the power button, mine at times only works on the bottom half of switch other times nothing happens for a few seconds. just an aside you say its not the battery. when you connect it to the charger do you see a battery graphic appear at all even for a few seconds. If not it might well be the battery.
The 5X is already being worked on by the Halium team, but is not generally recommended in the community due to its flash hardware defect. I've got one and I'm waiting for it to die in the next few months.